Rating: 
Summary: Differential Equations, RPI style
Review: This book was written by two RPI professors, Boyce and DiPrima, and is well-integrated into the RPI Intro to Differential Equations class. This book complements the class very well, and lectures help explain the material inside the book. However, that being said, I would have to say that if I were learning ODEs and PDEs on my own, that I would find this book difficult to use. The examples chosen are not what I would call the best for each section; however, the solutions manual covers many problems that the book decided to omit in their example portion of each section. This book makes ODEs and PDEs look much more difficult than they really are. Students don't benefit when the majority of the book is written in Greek (and yes, lambda and gamma make many appearances here) and the examples don't use specific numbers and instead use letters. Overall, if I hadn't taken a course using this book at RPI, I would have been clueless. Unless you're at RPI, I would stay away from this book.
Rating: 
Summary: A real mess
Review: this book's a mess. Especially if your instructor is messy too, the whole course will make no sense to you. I hope you won't have it assigned for your class, or else, buy some sort of study guide. This book alone does not have a clear outline. Good luck
Rating:
Summary: Expresses simple concepts in a formal,complicated manner
Review: This book, especially for the first 8 chapters, explains simple concepts in a difficult way. It is somewhat difficult to read, especially with all the formal notations, and often, it is impossible to tell what the author it trying to say. Some problems are ridiculously hard, requiring mathematical software in order to solve integrals. However, I found that the book does often review results, and this is useful. However, the examples are not the best, and are often too simple, and are missing most steps, which makes it almost impossible for a beginner student to understand.
Rating: 
Summary: Great Book, Can Be improved with a few more solved problems!
Review: This is as good as any book gets on this subject. I suggest you keep another book as backup for extra problems for you to work your way through. The explanations here are excellent, its just that there are too few solved examples to drill the idea into your head. But as far as understanding concepts goes, this is THE book on ODEs. Go for it!
Rating: 
Summary: The best mainstream ODE text
Review: This is the best mainstream book on (ordinary) Diff. Eqns. It is mainly oriented to engineers but a math major could benefit from it as well. Like most books on this subject it emphasizes on solving relatively small classes of Diff. Eqns, namely those that can be solved in closed form and like most of those books avoids, but not completely, the qualitative study of the subject. However, I believe that this is the best compromise of a "recipe book" and a book that really tries to encourage understanding of the subject. The book suffers from too many examples and pictures. The examples take too much space and have too many details. I can hardly blame the authors for this - they, and the publisher, just want to sell more books, and they have therefore to follow the general trend. You either have to write a book like this, or a real one, like Arnold's book, but that would be a book for a few only. "Proof" in Boyce-DiPrima is a dirty word but so is in any other mainstream text on Diff. Eqns. It was interesting to me to read most of the negative reviews here. Poor mathematical background makes many readers believe that the exercises are hard, the answers are put in weird form (meaning the reader has problems with middle school algebra), etc. If anything, many of the exercises are too easy. Those, who need Mathematica for solving integrals - you'd better retake your Calculus course. There are very few examples that really require Mathematica and they are mentioned clearly. Really interesting and challenging problems can be found sometimes but authors clearly understand that too many of those would hurt the sale numbers. One reader wrote: "This book makes ODEs and PDEs look much more difficult than they really are. " Well, like many other books, this book does not give you the slightest idea what ODEs and PDEs really are (try John's book as an introduction to PDEs), they are far more intellectually challenging and deep that most students can imagine. After so much negative comments, why do I still think that this is a good book? Because you cannot beat the system, at least this is not the way, and the math culture of most readers and students is not adequate to appreciate a real book (try Arnold). If you want a book that is still readable by the majority of the undergrad students, then this is the best one. If you want a real one, look elsewhere but do not complain that the author does not show the steps when solving a quadratic equation.
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